Standard airborne magnetic surveys are performed with sensors that measure the total magnetic intensity (TMI) which is the magnitude of the total magnetic field vector. The total field is assumed to comprise the earth's field added to a local field dependent on the geology. Survey areas are sufficiently small that the earth's field may be assumed constant and so all variations are due to the geology. In practice one subtracts the magnitude of the earth's field from the measured values to obtain the local field.
Of course, this practice is incorrect because it fails to allow for the fact that the magnetic field is a vector field. The simple subtraction of magnitudes is only correct when the two vectors (earth field and local field) are parallel. In general, remanence and anisotropy mean that parallelism is rarely achieved, however, for local fields that are small compared to the earth's field and close to parallel with it, the simple subtraction is a reasonable approximation.
In situations where the remanent magnetic field is comparable in size to the earth's field and in a variety of directions, the assumption is unreliable. The breakdown of this assumption will also affect fields derived from the TMI such as the reduced-to-pole (RTP) and first vertical derivative (1VD) fields.